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RESEARCH PAPERS

# Optimal Contact Force Distribution for Multi-Limbed Robots

[+] Author and Article Information
Dennis W. Hong1

Mechanical Engineering Department,  Virginia Tech, Blacksburg, VA 24061dhong@vt.edu

Raymond J. Cipra

School of Mechanical Engineering,  Purdue University, 585 Purdue Mall, West Lafayette, IN 47907-2088cipra@ecn.purdue.edu

1

Corresponding author.

J. Mech. Des 128(3), 566-573 (Jun 24, 2005) (8 pages) doi:10.1115/1.2179462 History: Received June 28, 2004; Revised June 24, 2005

## Abstract

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The incremental strategy of opening up the friction cones is aided by using the “force space graph” which indicates where the solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

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## Figures

Figure 11

The optimal solution (margin against slip criteria)

Figure 1

The force system

Figure 2

The force space graph representation

Figure 3

Valid∕invalid solution on the force space graph (a) a valid solution, (b) an invalid solution (slip at C1)

Figure 4

Defining margin against slip

Figure 5

Opening up the friction cones (a) PC1:PC2:PC3=1:1:1, (b) PC1:PC2:PC3=3:1:2

Figure 6

The solution volume representation

Figure 7

Finding the initial range for FC1α Using EC1* and EC2*

Figure 8

The FC2β, FC3γ range as a parallelogram (FC1α=0.907, no solution)

Figure 9

The first intersection between the (FC2β, FC3γ) parallelogram and the conic section EC3*(FC1α=1.211)

Figure 10

Optimal solution shown in the force space graph

## Errata

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